Physical review. B, Condensed matter

Exact-eigenstates study of the disordered Hubbard model

Avinash Singh

Published Jan 1, 1988• 9 citations

Abstract

The static magnetic susceptibility of the disordered Hubbard model for the half-filled-band case is studied using exact eigenstates of the noninteracting disordered system. The macroscopic renormalization-group method is applied to study the critical behavior in the vicinity of the noninteracting (Anderson) fixed point. A weak Hubbard interaction is found to stabilize the metallic phase.

DOI: 10.1103/physrevb.37.430

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Physical review. B, Condensed matter

Exact-eigenstates study of the disordered Hubbard model

Avinash Singh

Published Jan 1, 1988• 9 citations

Publisher

Abstract

DOI: 10.1103/physrevb.37.430

Related papers

Phase diagram of the two-dimensional Anderson-Hubbard model

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We investigate the single-band Hubbard model with random site energies in the strong-repulsion limit, as represented by the slave-boson formulation of the t-J model. It is essential to include the correlations between the slave-boson mean field and the disorder. This leads to the widening of the non-Fermi-liquid (``generalized Mott insulating'') region around half filling. In the Fermi-liquid regime we apply the renormalization-group method. The resulting phase diagram has superconducting, magnetic, and insulating phases. The disorder generally suppresses superconductivity and gives rise to the formation of localized magnetic moments.We investigate the single-band Hubbard model with random site energies in the strong-repulsion limit, as represented by the slave-boson formulation of the t-J model. It is essential to include the correlations between the slave-boson mean field and the disorder. This leads to the widening of the non-Fermi-liquid (``generalized Mott insulating'') region around half filling. In the Fermi-liquid regime we apply the renormalization-group method. The resulting phase diagram has superconducting, magnetic, and insulating phases. The disorder generally suppresses superconductivity and gives rise to the formation of localized magnetic moments.

Physical Review LettersMay 28, 199044 citations

{\mathit{U}}_{\mathit{c}}

. Away from half filling, the insulating phase is always gapless and is found to be controlled by the Anderson fixed point at half filling. This result is similar to that obtained in the corresponding one-dimensional system and suggests strongly the importance of the electron-electron correlation in this gapless insulating phase.

U

reaches a critical value

U_c

. Away from half filling, the insulating phase is always gapless and is found to be controlled by the Anderson fixed point at half filling. This result is similar to that obtained in the corresponding one dimensional system and suggests strongly the importance of the electron-electron correlation in this gapless insulating phase.

We study the half-filled Hubbard model with random on-site energies with the use of a real-space renormalization group. For

d=1

, we find a transition from an Anderson insulator to a Hubbard insulator as the Hubbard

U

is increased. We find no metallic phase. For

d=3

, we find a metallic phase which, surprisingly, is stabilized against Anderson localization by a small Hubbard

U

{\mathit{U}}_{\mathit{c}}

for a gap opening at the Fermi level in both two and three dimensions. This allows us to determine a phase diagram of the model that separates a Mott-Hubbard insulating phase and an unspecified gapless phase. The critical

{\mathit{U}}_{\mathit{c}}

line grows with disorder and tends to be linear for large enough W. Our results are consistent with previous real-space renormalization-group studies.

{\mathit{k}}_{\mathit{F}}

indicate that this quantity, which is the fastest diverging susceptibility of the pure system, diverges as T\ensuremath{\rightarrow}0 also when there is randomness in the hopping matrix elements, but not in the presence of random potentials. Both types of disorder cause a divergence of the uniform magnetic susceptibility. However, for random potentials a finite critical strength of the disorder appears to be required. At half-filling the transition from Mott (gapped) to Anderson (gapless) insulating behavior has been studied. A critical disorder strength is needed to destroy the gap, in agreement with Ma's renormalization group calculations.